Chinstrap Penguins
Nov 25, 2024
Chinstrap penguins are one of the most abundant penguin species in the Antarctic, with an estimated population of nearly eight million pairs. They are the most abundant penguin species breeding at the South Sandwich Islands. According to the study, the penguins take more than 10,000 naps a day, with each one lasting only four seconds, totaling 11-12 hours per day. Today we will analyze flipper lengths for Chinstrap penguins.
Image Source: Gemini AI
Y_i|\mu \sim N(\mu, \sigma^2)
Since flipper lengths are generally well-distributed and approximately normal for penguins, the Normal-Normal Bayesian Model is the most appropriate for the analysis of Chinstrap penguin flipper lengths.
Using prior studies we have determined the average flipper length of Chinstrap penguins is 193.37mm with a standard deviation of 6.12 [1]
Image Source: wikipedia.org
\mu \sim N(193.7, {6.12}^2)
| Model | Mean | Mode | Variance | SD |
|---|---|---|---|---|
| Prior | 193.37 | 193.37 | 37.4544 | 6.12 |
| Posterior | 195.7721 | 195.7721 | 0.7329711 | 0.8561373 |
95\% \text{ CI} = [194.08, 197.46]
Image Source: commons.wikimedia.org
Is the average flipper length for Chinstraps between 215 and 225mm?
Null Hypothesis H_0:
Alternative Hypothesis H_1:
Image Source: Gemini AI
The 95% credible interval for the posterior is [194.08, 197.46], which does not overlap with the range specified in the null hypothesis [215, 225]. This indicates the posterior belief supports values below 215mm, resulting in no evidence for the null hypothesis.
Image Source: crittersquad.com
Image Source: redbubble.com
| Hypotheses | Prior Probability | Posterior Probability |
|---|---|---|
| H_0: \mu \in (215,225) | P[H_0] = 0.9998 | P[H_0 \mid Y = 68] = 1 |
| H_1: \mu \notin (215,225) | P[H_1] = 0.0002 | P[H_1 \mid Y = 68] = 0 |
Image Source: Gemini AI
Image Source: Gemini AI
Image Sources: Palmer Station Antarctica LTER, Google Maps